Fr Kennedy made the announcement on Sunday following a mediation deal agreed with the archdiocese on Thursday, under which he will now hold his final Mass at St Mary's church on April 19, the ABC reports.
But St Mary's community council chairwoman Margaret Ortiz said that the community believed the process had been "unjust and unfair."
"The community also strongly believes Peter Kennedy has not caused ecclesiastical harm," she said.
Fr Kennedy on Sunday told reporters he expected the vast majority of St Mary's congregation to go with him to the new community, to be called "St Mary's In Exile".
"I could be wrong but I would expect about 95 percent to come. It's very gracious of the Trades and Labour Council to invite us," Fr Kennedy said, according to The Age.
"I'm hoping that somehow people within the community will come up with some ideas about how we might rent. We couldn't buy one, but we could rent something."
"For now, nothing has changed in my position, except I can't now come to St Mary's."
Fr Kennedy said he was still a Catholic priest with the right to conduct masses and baptisms.
Initially masses will be held at the Trades and Labor Council building but this would not be the new community's permanent home, and the hunt was on to find a place to rent, Fr Kennedy said.
Fr Kennedy will begin holding Mass at the new location on April 20, starting with a march from St Mary's.
"I think we've lost the fight by being pushed out of here, by being excluded from here, but have they won the battle? That is the question," Fr Kennedy said.
The Trades and Labour Council building will be refit prior to becoming the new temporary base.
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